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Extending work of Saneblidze–Umble and others, we use diagonals for the associahedron and multiplihedron to define tensor products of𝐴∞-algebras, modules, algebra homomorphisms, and module morphisms, as well as to define a bimodule analogue of twisted complexes (typeDDstructures, in the language of bordered Heegaard Floer homology) and their one- and two-sided tensor products. We then give analogous definitions for 1-parameter deformations of𝐴∞-algebras; this involves another collection of complexes. These constructions are relevant to bordered Heegaard Floer homology.
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This content will become publicly available on October 30, 2026
A continuous associahedron of type A
Abstract Taking a representation-theoretic viewpoint, we construct a continuous associahedron motivated by the realization of the generalized associahedron in the physical setting. We show that our associahedron shares important properties with the generalized associahedron of typeA. Our continuous associahedron is convex and manifests a cluster theory: the points which correspond to the clusters are on its boundary, and the edges that correspond to mutations are given by intersections of hyperplanes. This requires development of several methods that are continuous analogues of discrete methods. We conclude the paper by showing that there is a sequence of embeddings of typeAgeneralized associahedra into our continuous associahedron.
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- Award ID(s):
- 2452179
- PAR ID:
- 10701399
- Publisher / Repository:
- Springer Nature Link
- Date Published:
- Journal Name:
- Mathematische Zeitschrift
- Volume:
- 312
- Issue:
- 1
- ISSN:
- 0025-5874
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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